Transmission quality between a mobile phone and another mobile phone or a base station varies over time. Among the causes of such variation in transmission quality is the environment; thus, for example, obstacles of different kinds, shape and composition can divide the signal into multiple paths having different attenuation and length between the transmitting device and the receiving device. The relative movements of the transmitter and/or the receiver also contribute to temporal variations or “fading”. The propagation of the signal may vary between good and poor even on a packet basis.
One method for overcoming fading is to increase the transmit diversity, which is a measure of the number of antennas concurrently transmitting the signal. Thus, if two antennas are redundantly transmitting the same information, the transmit diversity is two. The quality of transmission can vary over time due to fading but, due to their different spatial locations, one of the two antennas is likely, at any particular moment, to be transmitting better than the other antenna. The receiver can take advantage of this by accepting the signal from an antenna with a strong transmitting signal while excluding the redundant, degraded copy of the signal from the other antenna which is transmitting on a weaker channel.
A transmit diversity method by which two transmit antennas redundantly send information to a single receiving antenna is disclosed in U.S. Pat. No. 6,185,258 to Alamouti et al., which is incorporated herein by reference. Information is transmitted temporally during “time slots”, the duration of which is small enough so that the transmission quality on each of the two channels is effectively constant during the time slot. A time slot is divided into symbol periods, each symbol period representing the time in which a single symbol is transmitted from an antenna. Under the Alamouti transmit diversity scheme, in a time slot having a duration of two symbol periods, a first antenna transmits a symbol z1 during the first symbol period and a symbol −z2* during the second symbol period, and a second antenna transmits a symbol z2 during the first symbol period and a symbol z1* during the second symbol period. Here, “a*” denotes the complex conjugate of “a”; i.e., if a=x+yj, then a*=x−yj. Time slots can be referred to as “time-space slots” in recognition that more than one antenna is transmitting —emphasizing that there is space diversity—or can simply be called “slots”. The Alamouti matrix CAla is shown below in equation (1), with each row corresponding to a transmit antenna and each column corresponding to a symbol period.                                           C                          A              ⁢                                                          ⁢              l              ⁢                                                          ⁢              a                                ⁡                      (                                          z                1                            ,                              z                2                                      )                          =                  [                                                                      z                  1                                                                              -                                      z                    2                    *                                                                                                                        z                  2                                                                              z                  1                  *                                                              ]                                    (        1        )            
If one of the two antennas is transmitting more robustly than the other during the time slot, both symbols can be derived solely from the stronger of the two transmissions. During the third and fourth symbol periods, a new slot is formed in which z3 assumes the role of z1 and z4 assumes the role of z2, and so on for subsequent time slots and respective symbol periods. Therefore, the transmit antennas transmit according to a sequence of 2×2 Alamouti codes. The kind of matrix, such as the 2×2 Alamouti matrix, that is used to represent transmit diversity over symbol periods is called a “space-time block code.” Here, the space-time block code and the time slot happen to coincide although, as discussed below, this is not always the case. The diversity here is two or “two-fold”, because each symbol is transmitted twice, by virtue of a delayed identical copy or delayed complex conjugate (or the negative of the complex conjugate or “negative complex conjugate”). Under the assumption that a single transmitter transmits one symbol per symbol period, the number of symbols that are transmitted per symbol period in a communication system is known as the “symbol rate”. The symbol rate here is one, since a symbol is considered to be the same, for this purpose, as its complex conjugate or negative complex conjugate.
A time slot in accordance with the Alamouti technique is an “orthogonal-based matrix”, which is defined here as a matrix that, when multiplied together with its Hermitian transpose, yields a real value times the identity matrix. The Hermitian transpose of a matrix A, denoted by AH, is a matrix whose elements are the complex conjugates of the elements of the transpose of A. The transpose of a matrix is derived by reversing the row and column designations of each element of the matrix. The identity matrix, denoted “I”, is a matrix with each element on its diagonal equal to unity and all other elements each to zero. Accordingly, for an orthogonal-based matrix A, it holds that AHA=AAH=k×I, for some real value k. The orthogonal-based property of the Alamouti matrix allows the transmission to be parsed into individual symbols by a single receiver.
The Alamouti transmit diversity method, however, assumes that little or no intersymbol interference (ISI) exists on the channel. ISI is a form of distortion in which the delay in the reception of one signal interferes with the ability of the receiver to distinguish a subsequently transmitted signal. The transmission of a symbol, for instance, may arrive by different paths at a receiver, and thus exhibit the phenomenon known as multipath. Most of the time, multipath is good because the arriving components are added to deliver greater signal strength. Although the different paths and resulting path lengths of the components cause different components to arrive at the receiver at a slightly different time, such differences in the time of receipt are generally not a problem; the radio waves propagate at virtually the speed of light, and the time differences are therefore small. The arrival time span is called the delay spread.
Delay spread does become a problem at higher symbol transmission rates because the ISI makes it difficult to detect individual arriving symbols at the receiver. An equalizer is often used to estimate the different components of a signal. To make the estimate, the equalizer is provided with training data on different paths and their relative timings and strengths. The training data may be in the form of pilot symbols that the equalizer knows ahead of time and receives with the transmission. The job of the equalizer is made easier by coding temporally adjacent symbols in such a way that respective components, when added (as through delay spread), can subsequently be separated. But if temporally adjacent symbols are redundant, i.e. because they are identical or complex conjugates, they are hard to separate at the receiver. The Alamouti technique transmits such temporally adjacent, redundant symbols and has empirically been found, on channels that experience ISI (i.e., ISI channels), to suffer from ISI distortion that renders transmit diversity ineffective.
Lindskog and Paulraj have proposed in “A Transmit Diversity Scheme for Channels with Intersymbol Interference”, Proc. IEEE ICC2000, 2000, vol. 1, pp. 307–311, an orthogonal-based, space-time block code that, unlike the Alamouti code, is effective on ISI channels. The Lindskog/Paulraj time slot is shown below in expression (2):                     [                                                            z                1                                                                    z                3                                                    …                                                      z                                                      2                    ⁢                    n                                    -                  1                                                                    pilots                                                      z                                  2                  ⁢                  n                                *                                                    …                                                      z                4                *                                                                                                                                        z                2                *                                                                                        z                2                                                                    z                4                                                    …                                                      z                                  2                  ⁢                  n                                                                    pilots                                                      -                                  z                                                            2                      ⁢                      n                                        -                    1                                    *                                                                    …                                                      -                                  z                  3                  *                                                                                                                                                        -                                  z                  1                  *                                                                    ]                            (        2        )            
In expression (2), the Alamouti code of equation (1) appears as the outermost nesting. That is, z1 and z2 are in the first symbol period, and the last symbol period is occupied by z2* and −z1* (with the negative signs switched, which still leaves the Alamouti matrix orthogonal-based). An Alamouti code corresponding to z3 and z4 is in the next most outer nesting, and so on for each subsequent symbol pair until z2n−1 and z2n. In expression (2), pilots refers to pilot symbols, which are added in a predefined place (here, in the middle of the time slot) and are used by the receiver to estimate characteristics of the channel as a means by which to reassemble signal components and thereby detect the transmitted symbols.
The main design criterion is to separate the two Alamouti symbol periods in an Alamouti slot into different halves of the Lindskog/Paulraj time slot, so that the transmission of a symbol and its complex conjugate is separated by Ts/2, where Ts is the length of the Lindskog/Paulraj time slot, i.e., Ts=(2n symbol periods+pilot symbol periods), although preferably, and as seen in relation (2) above, the sequences of symbols transmitted in the right-hand side of the Lindskog/Paulraj time slot are time reversed. For transmission utilizing the Lindskog/Paulraj method, standard equalizers may be used to equalize the channels, and ISI is minimized to the extent that the separation of a symbol and its delayed copy exceeds the delay spread of the channel.
The Alamouti and Lindskog/Paulraj approaches, however, are based on orthogonal-based, space-time block codes, and are therefore limited as to symbol rate and transmit diversity. Both of these approaches have a symbol rate of one and a transmit diversity of one, and both are MISO (multiple input, single output). Adapting either method for use with more than two transmit antennas, i.e. MIMO (multiple input, multiple output), in a way that retains the orthogonal-based property of the code results in a still lower symbol rate and relinquishes the simple code form shown in equation (1). Increasing the number of receiving antennas in non-orthogonal-based systems (i.e., systems that are not orthogonal-based) to two would ordinarily afford the potential for a symbol rate as high as two. However, the orthogonal-based property of the Alamouti and Lindskog/Paulraj codes limits the symbol rate to far below two, even if the number of receiving antennas is increased to two.